The same drilling rig which appears in "Breaking the Ice" was scripted to reappear in ENT: "Impulse", as evidenced by the final draft script of that installment. However, the rig isn't actually shown in the final version of "Impulse".

In the alternate reality, a drilling rig was the primary weapon of Nero's ship, the Narada, which was actually a mining vessel. Nero used the drilling rig to drill down to the core of Vulcan, then dropped a "red matter" bomb down the hole. The red matter created a singularity at the center of the planet which would consume it. He tried the same thing against Earth, but the drilling rig was destroyed by Spock after he commandeered the Jellyfish, before it reached Earth's core. (Star Trek)